Orthogonal Polynomials and Quadrature Rules

TOMS726 is a FORTRAN77 library which computes recursion relationships for various families of orthogonal polynomials, as well as the abscissas and weights of related quadrature rules; the library is commonly called ORTHPOL, and is by Walter Gautschi.


TOMS726 is available in a FORTRAN77 version and a FORTRAN90 version.

Related Data and Programs:

TOMS655, a FORTRAN77 library which computes the weights for interpolatory quadrature rules.

TOMS793, a FORTRAN77 library which carries out Gauss quadrature for rational functions, by Walter Gautschi; this is ACM TOMS algorithm 793.


  1. William Cody, Kenneth Hillstrom,
    Chebyshev Approximations for the Natural Logarithm of the Gamma Function,
    Mathematics of Computation,
    Volume 21, Number 98, April 1967, pages 198-203.
  2. Walter Gautschi,
    On Generating Orthogonal Polynomials,
    SIAM Journal on Scientific and Statistical Computing,
    Volume 3, Number 3, 1982, pages 289-317.
  3. Walter Gautschi,
    Algorithm 726: ORTHPOL - A Package of Routines for Generating Orthogonal Polynomials and Gauss-Type Quadrature Rules,
    ACM Transactions on Mathematical Software,
    Volume 20, Number 1, March 1994, pages 21-62.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN77 source codes.

Last revised on 15 March 2008.